Participants to take an inner tube(s) levers and a patch kit, but always get them to swap the tube for speed (patch at lunch if you want) and tools[1]. No-one will mind waiting for a tube swap, it only takes 10 minutes even if you have to instruct the bike owner (and the crowd). I'd always deal with a tube for anyone in my ride group, it's not a selfless as it sounds rather it is just so much quicker, and you can get them to put wheel back and tighten axle from a liability point of view.
Don't be checking bikes for safety as has already been mentioned as you then might carry the can for anything that failed - and you'd not want to find at that point your liability insurance is worthless.
If you do not have any trusty friends (as in previous ride guest who had a clue) who are likely to be able to help/stay with a stranded rider then you need to say at the outset that anyone in trouble has to make their own way, but an easy option, if its possible, is to plan a circular route near a station or one along a rail line (that takes bikes easily?) then anyone stranded can easily make their own way home.
So a ride along a suitable railway route so that escape stations are convenient, or just spiral near a fixed point so heading back directly into the centre with a broken bike is easy. A ~3 mile radius gets a ~25m ride but with a favourable shortcut it's just the 3m back to start.
Oh and the following time do the ride in reverse, no-one will notice (or not care) and anyone who says 'oh no we've done this before' can just plan the next ride [2] All my beginner rides have always had bail out stations for riders who couldn't do as much as they thought, only occasionally did a mechanical mean a train was needed.
[1] My tools and usage:-
Multi tool, for through axles, occasionally fixing rattly loose thing. (used many times, ride buddies and random riders)
5Amp choccy block connector to give a better gear than random default of top or bottom if a rear cable snaps (3 times, 2 for ME!)
Tyre boot for tyre rips, but plastic fivers are supposed to work (once)
Quick chain links in 8,9,10 and 11 the chain tool is on my multi tool (twice, random folk)
Pump/co2/patches that you know are good - rather than the crap some folk think are good. (twenty/thirty times?)
Many tiny clip on 'be seen' lights, october ish onwards (after hour changes, every year for the last 10! same 2 buddies yearly..)
Zip ties for re-fixing mudguards (used weekly come autumn and the use of the winter bike) or as zip pulls.
that list takes up no space at all, other club/touring kit might [3]
[2] Tell them you'd love to go on one of their rides, they almost always back off rapidly but occasionally do step up as a navigator if not leader!
[3] Club issued kit or my distance kit
Space blanket if out in the sticks rather than in a town, tiny (Never used but know of them being usedx2)
First Aid kit (big and a bloody nuisance) never used thankfully
I carry spare gear and brake inners when touring, or longer rural rides (tiny size, and my shifter used to snap rear cable at the shifter)
(used to carry) Spare folding tyre on tour in the wilds, saved long walks (twice) and urban-ly maybe 6 times! (most folk do have better tyres now).
All unused threaded bosses on my bike usually have relevant fasteners fitted as spares for those that rattle off other bikes (used a few)